Method for non-invasively determining the relative levels of two biological substances

ABSTRACT

The method for non-invasively determining the relative levels of two substances present in a biological system includes the steps of extracting by reverse iontophoresis charged and uncharged substances from said biological system, and collecting said substances, analysing the collected amount of a first extracted substance and a second extracted substance and determining the extraction ratio of the first substance to the second substance to determine their relative levels in the biological system. When the first and second substances are both analytes susceptible to changes in their concentration in the biological system, this method provides information about the relative concentrations of the two substances in the biological system. When the first substance is an analyte susceptible to changes in its concentration in the biological system and the second substance has a substantially constant concentration in the biological system, the second subtance acts as an internal standard and the extraction ratio becomes a direct measurement of the physiological level of the first substance in the biological system. A iontophoretic sampling device for monitoring the relative levels of two substances present in a biological system is also disclosed.

FIELD OF THE INVENTION

The present invention concerns in a general manner a method fornon-invasively determining the relative levels of two substances presentin a biological system.

More particularly, the present invention relates to a method fordetermining the relative levels of two substances present in abiological system, using the technique of reverse iontophoresis, and toa iontophoretic sampling device for monitoring the relative levels oftwo substances present in a biological system.

DESCRIPTION OF THE RELATED ART

The detection and/or quantification of endogenous substances is a keyfactor in establishing a medical diagnosis.

Similarly, the detection and/or quantification of exogenous substancessuch as drugs, metabolites, and markers of therapeutic or toxic effectis a key factor to determine if a medical treatment is appropriate.

However, detection and/or quantification of endogenous or exogenoussubstances requires in a general manner a prior invasive blood samplingwith a needle, with the consequences that pain may accompany thesampling procedure and there may be a risk of bacterial or viralinfection for both patient and sampler.

An example where sampling of an endogenous substance is needed, at leastseveral times a day for life time, is in the case of patients havingsugar diabetes.

For these patients, real time information concerning the glucose levelsin the body is most important information in the patient's treatment andin many cases, often a question of life or death.

A non-invasive method known under the name of iontophoresis has beenused to achieve increased drug delivery across the skin for many years,and more recently it has been demonstrated that the symmetry of theprocedure also allows samples of circulating, biologically-importantions and uncharged molecules dissolved in a biological fluid to bewithdrawn from the subcutaneous space to the skin surface (a techniquereferred to generally as reverse iontophoresis).

The technique of iontophoresis may be defined as the enhanced transportof charged or uncharged molecules across biomembranes, in particularskin, under the influence of an electrical potential gradient.

The level of current necessary to enhance this transport is painless.

This technique avoids the need to puncture the skin and thereforereduces, tremendously, risks to both patient and sampler.

Iontophoresis uses a iontophoretic device consisting of a power supplyand two electrode compartments.

These compartments hold an electrode and, typically, an electrolytesolution or conductive hydrogel.

In the case of iontophoretic sampling, the electrode compartmentscontain an appropriate receiving medium, for example buffered saline,into which the analytes of interest are collected.

The electrode compartments may also contain the means with which toquantify the analyte(s) of interest in situ, or the contents of theelectrode compartment may be removed at certain predetermined times fordetermination of the analyte(s) in another apparatus.

Iontophoresis can be used successfully to withdraw, at significantlyelevated levels, both charged and uncharged molecules from within andbeneath the skin.

Iontophoretic transport through the skin involves two principalmechanisms.

One, so called electromigration, concerns only charged molecules and theother, so called electroosmosis or convective flow, can involve thetransport of both charged and uncharged molecules.

The electromigrative transport is a direct consequence of theinteraction of the electric field with ions.

When the electric field is applied, the cations contained in the anodalchamber are repelled from the anode toward and through the skin and theendogenous or exogenous cations are attracted into the cathodal chamber.

Consequently, an endogenous or exogenous cation will be collected intothe cathodal chamber.

On the same principle, anions are repelled from the cathodal chamber anddriven into and through the skin and the endogenous or exogenous anionsare attracted into the anodal chamber on the skin surface.

Consequently, endogenous or exogenous anions will be collected into theanodal chamber.

The electroosmotic transport is based on the fact that, at neutral pH,the skin is a negatively charged membrane, and is thereforepermselective to cations.

It follows that, on application of an electrical field, more charge iscarried across the skin by positive ions than by negative ions.

This means that more momentum is transferred to the solvent (i.e.,water) in the direction of cation movement so that uncharged moleculesare convected along with the flow of solvent at a rate which is, formany substances, significantly greater than that possible by passivediffusion.

Consequently, an endogenous or exogenous uncharged molecule will becollected into the cathodal chamber. Electroosmotic transport can beparticularly efficient for water-soluble, polar (yet uncharged)substances, as these compounds typically have very poor permeabilityacross the lipophilic (hydrophobic) skin barrier.

Further, the electroosmotic flow therefore assists the sampling ofcations while diminishing, to some extent, the sampling of anions.

When the iontophoretic device is activated, an electrical circuit isestablished.

The exterior part of the circuit involves electrons travelling along thewire from the anode to the cathode via the power supply and the interiorpart of the circuit involves the movement of ions from one electrodechamber to the other via the skin and the physiological medium.

The number of electrons flowing in the exterior part of the circuitdetermines the number of ions moving in the interior part.

Hence, the flux of ions is directly proportional to the total charge inCoulombs passed between the electrodes from the power supply.

It is known that the extraction of a substance to the skin surface byreverse iontophoresis is proportional to the subcutaneous level of thesubstance.

Reverse iontophoresis per se is not selective so that discriminationcomes at the level of the extracted sample.

Thus, a multiplicity of species can be withdrawn by iontophoresis andassayed specifically.

Based on these principles, U.S. Pat. No. 5,279,543, U.S. Pat. No.5,362,307 and U.S. Pat. No. 5,730,714, disclose methods fornon-invasively determining the level of a substance present in abiological system.

These methods comprise, in a general manner, contacting an anodalchamber and a cathodal chamber of an iontophoresis device with abiological system; extracting by reverse iontophoresis charged anduncharged substances from the biological system, and collecting saidextracted substances into the anodal or cathodal chamber; analysing thecollected amount of one of the extracted substances; and correlating thelevel of the analysed substance with a standard.

Based on these methods, U.S. Pat. No. 5,771,890, U.S. Pat. No. 5,989,409and U.S. Pat. No. 6,023,629 disclose particular methods for measuringthe concentration of a substance, in particular glucose, in a mammaliansubject.

However, in these methods, the level of the analysed substance iscorrelated with the level of the substance in the blood of the patient,so that a blood sampling is required.

A number of devices for non-invasively determining the level of asubstance present in a biological system based on these methods havebeen disclosed, most of them being provided for non-invasivelymonitoring glucose, as for example the device commercialised by Cygnus,Inc. ( Redwood City, Calif., USA), under the name GlucoWatch®Biographer.

However, these devices must be calibrated each time they are started,and each calibration requires blood sampling.

In view of the above, there is a need for a method and for a devicewhich does not require the comparison of the level of theiontophoretically extracted substance with a standard obtained from ablood sample and thus which would allow the monitoring of the level of asubstance in a biological system without a calibration based on a bloodsampling.

A preliminary study to ascertain whether tissue electrolytes may bedetermined by reverse iontophoresis was disclosed by F. B. Benjamin, R.Kempen, A. G. Mulder and A. C. Ivy. in Journal of Applied Physiology,vol. 6, pp. 401-407, 1954 “Sodium-potassium ratio of human skin asobtained by reverse iontophoresis”.

Experiments were performed in vivo and in vitro.

In vivo, the situation of greatest interest, a metal plate cathode wasused, being inserted into a lithium nitrate electrolyte solution (28.5mEq/L) on the skin surface.

The area of contact between the cathode solution and the skin was 4.5cm².

A current of 4 mA was passed for 5 minutes (and sometimes longer) andduring this time, the pH of the lithium nitrate solution increased from6.4 to 10.7, indicating hydrolysis of water at the cathode.

Skin damage was observed in some cases.

After current passage, the concentrations of potassium and sodium ionsin the cathode chamber were typically about 14 and 35 μEq/L,respectively.

The day of the measurement, the ambient temperature, the gender and ageof the subject, and the site of measurement on the body, did not affectsignificantly the results obtained.

The sodium to potassium ratio in the extraction solution was thereforeabout 2.5:1.

This ratio was compared to the relative composition of the ions in sweat(7.1:1), whole skin (6:1), epidermis (0.6:1), interstitial fluid (29:1)and intracellular fluid (0.03:1), and was clearly not consistent withany of these environments.

It was noted, however, that the extracted ratio did decrease in subjectsreceiving a low-sodium diet (to 2.0:1) and that it could also be lowered(again to 2.0:1) by blocking sweat secretion with atropine.

In neither case, though, did the ratio change to reflect the relativecomposition of the ions in any tissue of interest. Nor was any methodprovided that would allow the extracted ratio of ions to be relatedconsistently to their relative composition in any tissue of interest.

In vitro, the extraction was performed with hypertonic, isotonic andhypotonic saline solutions below the excised skin obtained from a humancadaver.

The type of solution used influenced the extraction results in the sameway as when similar solutions were injected intradermally in normalhuman subjects, in vivo.

Nevertheless, again, the ratio changes did not reflect quantitativelythe relative composition of the ions in any tissue of interest. Nor wasany method provided that would allow the extracted ratio of Ions to berelated consistently to their relative composition in any tissue ofinterest.

In summary, while this research purported to be useful for monitoringdisturbances in electrolyte balance in patients, and speculated aboutthe results being perhaps correlated with those of metabolic and bloodconcentrations, the results demonstrated in fact: (a) no agreementbetween the extracted sodium to potassium ratio and that in any tissuecompartment of interest, and (b) no suggestion that either ion, or anyother electrolyte or endogenous substance, for that matter, might beused as an internal standard for calibration-free, non-invasivebiosensing by reverse iontophoresis.

More recently, an attempt has been made to determine the concentrationof lactic acid on the dermal side of a iontophoretic cell by employingthe flux ratio of lactic acid and chloride ions (the chloride ion beinga constant level endogenous ion), as published by S. Numajiri, KSugibayashi and Y. Morimoto in “Journal of Pharmaceutical & BiomedicalAnalysis Vol. 11, No. 10; pp 903-909, (1993) (“Non-invasive sampling oflactic acid ions by iontophoresis using chloride ion in the body as aninternal standard”).

In this document, the results show that chloride ion flux decreases withan increase in lactic concentration and that the flux ratio of lacticacid/chloride ions is constant and is independent of the electricalpotential gradient thus meaning that the transport number of lactic acidis dependent on the transport number of chloride.

Since the flux ratio of lactic acid/chloride ions is constant, the fluxratio of lactic acid/chloride Ions does not provide a direct measure ofthe relative levels of these two substances in the dermis side of thecell and further does not provide a direct measure of the physiologicallevel of lactic acid in the dermis side of the cell.

Furthermore, in this document, two features of the experimentalprocedure used render the feasibility of the method at bestquestionable.

First, the level of current used to extract the ions of interest acrossthe skin was either 2.1 mA/cm² or 3.2 mA/cm², that is, more than 4 or 6times, respectively, the current density considered the maximumtolerable limit (0.5 mA/cm²) for iontophoresis in vivo, in humans.

Second, platinum electrodes were utilised in the experiments reported.

It is well-established in the literature that the electrochemistry atplatinum electrodes causes hydrolysis of water, liberating eitherhydronium cations or hydroxide anions into the electrode solutions witha considerable risk, therefore, of dramatic changes in pH.

Together with the high current densities used, as well, a significantprobability of skin irritation and/or burns is evident from theprocedure as described.

In addition, hydronium cations and hydroxide anions are small and verymobile, and they are efficient charge carriers in iontophoresis; theirincreasing presence in the electrode solutions will compete effectivelywith the ions of interest to carry charge across the skin, and willtherefore further change the transport numbers of chloride and lacticacid ions, rendering useless the value of the method proposed.

An object of the present invention is to propose a method fordetermining the relative levels of two substances present in abiological system by avoiding blood sampling when only the relativeconcentration of two molecules is of interest.

A further object of the present invention is to propose a method whereinthe relative levels of a first extracted substance present in abiological system with respect to a second extracted substance presentin the biological system is a direct measure of the physiological levelof the first substance, thus avoiding a calibration based on a bloodsampling.

A still further object of the present invention is to propose a devicewhich allows the monitoring of the relative levels of two substancespresent in a biological system without a calibration based on a bloodsampling.

A still further object of the present invention is to propose a devicewhich allows the monitoring of the physiological level of a substancepresent in a biological system without a calibration based on a bloodsampling.

According to the present invention, these objects have been achieved asa result of the unexpected findings that when two substances extractedfrom a biological system by reverse iontophoresis have independentrespective transport and/or transference numbers, the ratio of therespective extracted amounts or the ratio of their flux is a directmeasure of the relative levels of the two substances in the biologicalsystem.

SUMMARY OF THE INVENTION

According to one aspect, the present invention concerns a method fornon-invasively determining the relative levels of two substances presentin a biological system, said method comprising:

-   -   contacting an anodal chamber and a cathodal chamber of an        iontophoresis device comprising reversible electrodes with a        biological system;    -   extracting by reverse iontophoresis charged and uncharged        substances from said biological system, and collecting said        charged and uncharged substances each independently into the        anodal chamber or the cathodal chamber;    -   analysing the collected amount of at least a first extracted        substance and a second extracted substance; wherein said first        and second substances are selected in such a way that the        transport and/or transference number of the first substance is        independent of the transport and/or transference number of the        second substance;    -   subsequently, determining the extraction ratio of the first        substance to the second substance to determine their relative        levels in the biological system.

According to the method of present invention, when the first substanceand the second substance are both analytes susceptible to changes oftheir concentration in the biological system, the determined extractionratio provides information about the relative concentrations of the twosubstances in the biological system.

In this case, the ratio may be advantageously used to establish adiagnostic of any physiological or pathological condition, in which theratio of two endogenous or exogenous analytes is of relevance, withoutrequiring a blood sampling.

Further, according to the method of the present invention, when thefirst substance is an analyte susceptible to changes in itsconcentration in the biological system and the second substance has asubstantially constant concentration in the biological system, thesecond substance acts as an internal standard and the extraction ratiobecomes a direct measurement of the physiological level of the firstsubstance in the biological system.

In this case, the extraction ratio may be advantageously used toestablish a diagnostic of any physiological or pathological condition,in which the physiological level of the endogenous or exogenous analyteis of relevance, without requiring a blood sampling.

According to a further aspect, the present invention provides aiontophoretic sampling device for non-invasively monitoring the relativelevels of two substances present in a biological system, said devicecomprising:

-   -   an electrical power supply,    -   a collection assembly comprising a first collection chamber        containing a first electroconductive medium in contact with a        first electrode and a second collection chamber containing a        second electroconductive medium in contact with a second        electrode, said first and second electrodes being reversible        electrodes and being each in contact with the electrical power        supply when the collection assembly is inserted in the        iontophoretic device;    -   a means for analysing two or more selected charged and/or        uncharged substances in either one or both of the collection        chambers in order to determine their extracted amounts,    -   a means for converting the extracted amounts of a first        substance and a second substance to the extraction ratio of the        first substance to the second substance, wherein said first and        second substances are selected in such a way that the transport        and/or transference number of the first substance is independent        of the transport and/or transference number of the second        substance.

According to the iontophoretic sampling device of the present invention,when the first substance and the second substance are both analytessusceptible to changes in their concentration in the biological system,the determined extraction ratio provides information about the relativeconcentrations of the two substances in the biological system.

In this case, the extraction ratio may be advantageously used toestablish a diagnostic of any physiological or pathological condition,in which the ratio of two endogenous or exogenous analytes is ofrelevance, without requiring a blood sampling.

Further, according to the iontophoretic sampling device of the presentinvention, when the first substance is an analyte susceptible to changesin its concentration in the biological system and the second substancehas a substantially constant concentration in the biological system, thesecond substance acts as an internal standard and the extraction ratioprovides a direct measurement of the physiological level of the firstsubstance in the biological system.

In this case, the extraction ratio may be advantageously used toestablish a diagnostic of any physiological or pathological condition,in which the physiological level of the endogenous or exogenous analyteis of relevance, without requiring a blood sampling.

Other advantages of the present invention will appear in the followingdetailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic view of a known iontophoretic device for usefor in vivo sampling of charged or uncharged substances.

FIG. 2 shows a schematic view of a known iontophoretic device for themodeling in vitro of iontophoretic sampling of charged or unchargedsubstances.

FIG. 3 represents a specifically-designed iontophoresis cell used forthe in vitro experiments reported in Example 1.

FIGS. 4 a-b represent the extraction fluxes of valproate and glutamateat 5 hours and 24 hours as obtained in the in vitro experiments reportedin Example 1.

FIGS. 5 a-b represent the transport numbers of valproate and glutamateat 5 hours and 24 hours as obtained in the in vitro experiments reportedin Example 1.

FIG. 6 a shows the linear correlation obtained between the extractionratio (valproate/glutamate) and the valproate concentration in thesub-dermal solution as obtained in the in vitro experiments reported inExample 1.

FIG. 6 b shows the linear correlation obtained between the extractionratio (valproate/glutamate) and their molar ratio (valproate/glutamate)in the sub-dermal solution as obtained in the in vitro experimentsreported in Example 1.

FIG. 7 represents a specifically-designed iontophoresis cell used forthe in vitro experiments reported in Example 2.

FIGS. 8 a-b represent the extraction fluxes of lactate, ammonium,potassium, sodium and chloride at the 3^(rd) hour and 5^(th) hour of theexperiments reported in Example 2.

FIGS. 9 a-b represent the transport numbers of the two analytes ofinterest (lactate and ammonium) and of the three internal standardsconsidered (K⁺, Na⁺Cl⁻) as obtained from the experiments reported inExample 2

FIGS. 10 a-b represent the extraction ratio of the couples of substances[a] (ammonium/sodium), [b] (ammonium/potassium), [c] (lactate/chloride),[d] (lactate/sodium), [e] (lactate/potassium) and [f] (potassium/sodium]as obtained from the experiments reported in Example 2.

FIG. 11 represents a specifically-designed iontophoresis cell used forthe in vitro experiments reported in Example 3.

FIG. 12 represents the fluxes of mannitol and sodium over the six hoursof the experiments reported in Example 3, first experiment.

FIG. 13 represents the correlation between the iontophoretic extractionratio of mannitol to sodium and their sub-dermal concentration ratioover the six hours of the experiments reported in Example 3, firstexperiment.

FIGS. 14 a-b represent the fluxes of mannitol and sodium and the(mannitol/sodium) extraction flux ratio over the 5 hours of theexperiments reported in Example 3, second experiment.

FIGS. 15 a-b show the correlation between the iontophoretic extractionratio of mannitol to sodium and [a] the mannitol sub-dermalconcentration, and [b] the sub-dermal concentration ratio(mannitol/sodium) over the 5-hour period of the experiments reported inExample 3, second experiment.

FIG. 16 represents a specifically-designed iontophoresis cell used forthe in vitro experiments reported in Example 4.

FIGS. 17 a-b show the fluxes of mannitol and sodium and the(mannitol/sodium) extraction flux ratio over the 6 hours of theexperiments reported in Example 4.

FIG. 18 shows the correlation between the iontophoretic extraction ratioof mannitol to sodium and the mannitol sub-dermal concentration over the6-hour period of the experiments reported in Example 4.

FIG. 19 shows the fluxes of glucose and sodium over the 6 hours of theexperiment reported in Example 5.

FIG. 20 shows the (glucose/sodium) extraction flux ratio over the 6hours of the experiment reported in Example 5.

FIGS. 21 a-c show the fluxes of glucose, mannitol and sodium during the6-hour periods of Experiments A, B and C, respectively, reported inExample 6.

FIG. 22 a shows the correlation between (a) the iontophoretic extractionratio of glucose to sodium and the glucose sub-dermal concentration, and(b) the iontophoretic extraction ratio of mannitol to sodium and themannitol sub-dermal concentration, following 6 hours iontophoresis at0.5 mA/cm², as reported in Example 6.

FIG. 22 b shows the correlation between (a) the iontophoretic extractionratio of glucose to sodium and the sub-dermal concentration ratio(glucose/sodium), and (b) the iontophoretic extraction ratio of mannitolto sodium and the sub-dermal concentration ratio (mannitol/sodium),following 6 hours iontophoresis at 0.5 mA/cm², as reported in Example 6.

FIG. 22 c shows the correlation between the iontophoretic extractionratio of glucose to mannitol and the sub-dermal concentration ratio(glucose/mannitol), following 6 hours iontophoresis at 0.5 mA/cm², asreported in Example 6.

FIG. 23 represents a specifically-designed iontophoresis cell used forthe in vitro experiments reported in Example 7

FIGS. 24 a-b show (a) the extraction fluxes of lithium and sodium and(b) the (lithium/sodium) extraction flux ratios, over the 5 hours ofexperiment reported in Example 7, for each sub-dermal lithiumconcentration considered.

FIGS. 25 a-b show the correlation between the iontophoretic extractionratio of lithium to sodium and [a] the lithium sub-dermal concentration,and [b] the sub-dermal concentration ratio (lithium/sodium) over the5-hour period of the experiment reported in Example 7.

FIG. 26 shows the simultaneous extraction of glucose and sodium in vivoin a human being, and the correlation with the concentration of glucosein the blood.

DETAILED DESCRIPTION OF THE INVENTION

The present invention will now be described in a more detailed manner,referring to FIGS. 1 and 2.

Formally, the method of the present invention may be divided in threedistinct phases including:

-   -   the extraction of charged and uncharged substances from a        biological system by reverse iontophoresis including collection        of these substances;    -   the selection of at least two collected substances to be        analysed and the analysis of said selected substances by using        appropriate analytical chemistry techniques, to determine their        respective extracted amounts;    -   the determination of the extraction ratio of the two analysed        substances, based on the analysis results to evaluate their        relative levels in the biological system.

According to the method of the present invention the first phase ofextraction and collection of the extracted substances includes the stepsof

-   -   contacting an anodal chamber and a cathodal chamber of an        iontophoresis device comprising reversible electrodes with a        biological system;    -   extracting by reverse iontophoresis charged and uncharged        substances from said biological system, and collecting said        charged and uncharged substances each independently into the        anodal chamber or the cathodal chamber.

A iontophoretic device which can be used in the method of the presentinvention may be any conventional iontophoretic device comprising apower supply connected to an anodal chamber and to a cathodal chamber,wherein said chambers contain each an appropriate receivingelectroconductive medium provided to collect the substances of interest.

An example of a iontophoretic device which can be used for theextraction and the collection of the substances from a biological systemaccording to the method of the present invention comprises, asrepresented schematically in FIG. 1, a first chamber 1 containing afirst receiving electroconductive medium 2 and a second chamber 3containing a second receiving electroconductive medium 4.

The receiving electroconductive media 2 and 4 may be each independentlyselected from a liquid, a gel, a paste, a sponge, a ceramic or acombination thereof. A negative electrode or cathode 5 is immersed inthe first receiving electroconductive medium 2 contained in the chamber1 so that the chamber 1 is referred to as cathodal chamber 1.

A positive electrode or anode 6 is immersed in the second receivingelectroconductive medium 4 contained in the chamber 3 so that thechamber 3 is referred to as anodal chamber 3.

The physical form of the electrodes (cylinder, sphere, disk, mesh,screen-printed, etc.) is chosen for convenience and practicality.

The cathode 5 and the anode 6 are each connected to a power supply 7 bywires.

The iontophoretic device used in the method of the present inventioncomprises reversible electrodes in order to avoid water hydrolysis.

More preferably, the iontophoretic device used in the method of thepresent invention comprises Ag/AgCl electrodes.

The anode and cathode electrode reactions are, respectively:anode: Ag⁰ (s)+Cl⁻(aq)→AgCl (s)+écathode: é+AgCl (s)→Ag⁰ (s)+Cl⁻(aq)and are exactly opposite to one another.

Should it prove advantageous, therefore, to alternate the polarity ofthe electrodes during a reverse iontophoresis extraction procedure (asis the case, for example, in the GlucoWatch® Biographer of Cygnus,Inc.), the Ag/AgCl electrodes are ideal.

The cathodal chamber 1 and the anodal chamber 3 are each in closecontact with a biological system 8.

The modeling in vitro of the extraction and collection of substancesfrom a biological system according to the method of the presentinvention may be performed for example using the iontophoretic devicerepresented schematically in FIG. 2, which comprises, similarly to theiontophoretic device represented in FIG. 1, a cathodal chamber 1′containing a first receiving electroconductive medium 2′, an anodalchamber 3′ containing a second receiving electroconductive medium 4′, acathode 5′ immersed in the receiving medium 2′ contained in the cathodalchamber 1′, an anode 6′ immersed in the receiving medium 4′ contained inthe anodal chamber 3′, and a power supply 7′ connected to both thecathode 5′ and the anode 6′.

However, to simulate the biological system, this device, which will bereferred to below as an in vitro iontophoretic device, will comprise,instead of the biological system, a container 9 containing anelectroconductive donor solution 10 such as a physiological buffercontaining the substances to be extracted, said container being closedin its upper part by a piece of a mammalian skin 11.

The container 9 may further comprise a circulation system 12 of thedonor solution 10 to maintain constant, or to vary in a controlledfashion, the concentration of the substances contained in the donorsolution 10.

In this in vitro iontophoretic device, the cathodal chamber 1′ and theanodal chamber 3′ are each in close contact with the mammalian skin 11.

Such devices are for example disclosed in U.S. Pat. No. 5,279,543, U.S.Pat. No. 5,362,307, U.S. Pat. No. 5,730,714, U.S. Pat. No. 6,059,736,U.S. Pat. No. 5,771,890, U.S. Pat. No. 6,023,629.

In the method of the present invention, the cathodal chamber 1containing the first receiving electroconductive medium 2 and the anodalchamber 3 containing the second receiving electroconductive medium 4 ofthe iontophoretic device as represented in FIG. 1 are first contactedwith the biological system 8.

Preferably, the biological system is a human body so that the cathodalchamber 1 and the anodal chamber 3 will be in contact with skin ormucosal tissues.

Then a current is applied during a determined time by means of the powersupply 7 to establish an electric circuit.

According to the present invention, the current density may range from0.01 to 1.00 mA/cm², depending on the biological system.

Preferably, the current density should not be higher than 0.5 mA/cm²when the biological system is a human body, since levels higher than 0.5mA/cm² may cause unpleasant sensation or pain.

A more preferred current density applied when the biological system is ahuman body is about 0.3 mA/cm². The exterior part of the circuitinvolves electrons travelling along the wire from the anode 5 to thecathode 6 via the power supply 7 and the interior part of the circuitinvolves the movement of ions from one electrode chamber to the othervia the biological system 8.

Thus, due to this circuit, cations move from the anode 6 to the cathode5 via the biological system 8 under a mechanism of electromigrativetransport assisted by electroosmotic transport, anions move from thecathode 5 to the anode 6 via the biological system 8 under a mechanismof electromigrative transport, and counter to electroosmotic flow, anduncharged molecules move in same direction as the cations from the anode6 to the cathode 5 via the biological system 8 under electroosmotictransport.

As a consequence, cations are extracted from the biological system 8 andare collected into the cathodal chamber 1, anions are extracted from thebiological system 8 and are collected into the anodal chamber 3, anduncharged substances are extracted from the biological system 8 andcollected into the cathodal chamber 1.

An advantageous effect of extracting substances by reverse iontophoresisis that the collected samples are free of proteins and of variouscellular or tissue debris because proteins and various debris areblocked by the skin and retained in the biological system.

Similarly, an in vitro iontophoretic device as represented by FIG. 2 maybe used for modeling the extraction and the collection of substancesaccording to the method of the present invention.

In this case, cations are extracted from the donor solution 10 acrossthe piece of mammalian skin 11 and are collected into the cathodalchamber 1′, anions are extracted from the donor solution 10 via thepiece of mammalian skin 11 and are collected into the anodal chamber 3′,and uncharged substances are extracted from the donor solution 10 acrossthe piece of mammalian skin 11 and are collected into the cathodalchamber 1′.

As iontophoresis per se is not selective, iontophoretic extraction leadsto the collection of a number of different molecules including ions anduncharged molecules dissolved in the biological system.

After the first phase of extraction of charged and uncharged substancesfrom the biological system by reverse iontophoresis and the collectionof these extracted substances in the collection chambers 1 and 3; themethod of the present invention comprises the second phase of selectionof two extracted substances for which the extraction ratio is to bedetermined, and the analysis of these two collected substances usingappropriate analytical chemistry techniques including the use ofspecific biosensors and biosensing methods to determine their respectiveextracted amounts.

Since iontophoresis per se is not selective, discrimination of the pairof substances for which the relative levels in the biological system areto be determined is achieved at the level of the analysis of thecollected substances.

Accordingly, the second phase of the method of the present inventioncomprises the step of analysing the collected amount of a firstextracted substance and of a second extracted substance.

According to the present invention, an essential feature is that thefirst and second substances must be selected in such a way that thetransport and/or transference number of the first substance isindependent of the transport and/or transference number of the secondsubstance.

In the present invention, the pair of substances whose relative levelsare to be determined is selected depending on the desired objectives.

If only the relative concentration of the two substances in thebiological system is of interest, the first substance and the secondsubstance may be selected to be both susceptible to changes in theirconcentration.

In this case, the extraction ratio only provides information about therelative systemic concentrations, not about the respective “real”concentrations.

An advantageous use of such a selection may be for example when theratio between two molecules may give indications of a pathologic stateor a disease.

However, in a particularly preferred embodiment of the invention, thefirst substance is selected to be a substance of interest susceptible tochanges in its concentration in the biological system and the secondsubstance is selected to have a substantially constant concentration inthe biological system and consequently a substantially constantiontophoretic extraction flux so that the extraction ratio between thefirst substance and the second substance varies essentially linearlywith the concentration of the first substance.

In this case, the second substance acts as a physiological internalstandard and the extraction ratio becomes a direct measurement of thephysiological level of the first substance (analyte) in the biologicalsystem.

This may be explained as follows.

The iontophoretic flux of a substance included in a ionic solution suchas the physiological medium is proportional to the concentration of thatsubstance.

It follows that the iontophoretic flux of the internal standard remainspractically constant.

On the other hand, the extraction of the analyte will vary according toits concentration in the body.

It follows that the ratio of the extracted substances should beproportional to their relative internal concentrations.

This advantageous embodiment allows determination of the realconcentration of the analyte in the biological system while avoidingblood sampling, as illustrated below.

In a preferred embodiment, the first substance and the second substanceare collected in the same collection chamber.

This preferred embodiment is achieved when the first substance and thesecond substance are either two anions, or two cations, or one neutralmolecule and one cation, or two neutral molecules.

For example, according to this preferred embodiment, monitoring of theconcentration of glucose, a neutral molecule, as the analyte may beperformed by using sodium, a cation, as the physiological standard, thusavoiding the sampling of blood several times a day for patients havingsugar diabetes.

However, in the case where the first substance is an analyte and thesecond substance is an internal standard, and that the analyte and theinternal standard are an anion and a cation, or an uncharged moleculeand an anion, this preferred embodiment may be achieved by reversing thepolarity of the current applied.

However, it should be noted that reversing polarity may be also usedwhen the analyte and the internal standard are either two anions, or twocations or one neutral molecule and one cation.

As an example of an iontophoretic extraction wherein polarity isreversed during the extraction procedure, current is first applied asdisclosed above during a first determined time by means of the powersupply 7 to establish the electric circuit. As a consequence, cationsare collected into the cathodal chamber 1, anions are collected into theanodal chamber 3, and uncharged substances are collected into thecathodal chamber 1.

Then, the polarity is reversed and current is applied during a seconddetermined time to establish an inverted electric circuit, wherein theelectrode 5 becomes an anode, and the electrode 6 becomes a cathode.

Thus, due to this inverted circuit, the cations move from the electrode5 to the electrode 6 via the biological system 8, the anions move fromthe electrode 6 to the electrode 5 via the biological system 8 and theuncharged molecules move in same direction as the cations from theelectrode 5 to the electrode 6 via the biological system 8.

This means that due to this inversion of polarity, cations are collectedinto the collection chamber 3, anions are collected into the collectionchamber 1, and uncharged substances are collected into the collectionchamber 3.

As a consequence, cations and uncharged molecules and then anions arecollected sequentially into the chamber 1, anions and then cations anduncharged molecules are collected sequentially into the chamber 3.

Advantages to collect the analyte and the internal standard in the sameelectrode chamber are to assure that the extraction of the twosubstances (analyte and internal standard) occurs across exactly thesame skin surface and to obviate any problems associated withsite-to-site differences in the properties of the skin; and to allow allthe electro- and analytical chemistries necessary to be contained withinthe one chamber.

Further, if reversing the polarity is used between eachiontophoresis/analysis cycle, then both electrode formulations can beidentical, facilitating the manufacturing/assembly process; andsimilarly, with reversing polarity and Ag/AgCl electrodes, there is noconcern about build-up or depletion of AgCl at the anode and cathodeduring the course of the procedure.

Further, if continuous monitoring is not required, and analysis isperformed “off-line”, having both substances collected into the samereceiver simplifies subsequent processing.

Analysis of both the selected substances is performed using appropriateanalytical techniques including biosensing techniques to determine theamount of each extracted selected substance.

For example, the means of analysing both selected substances may involvespecific enzymes, ion-selective chemistry, measurement of conductivityand all other known analytical chemistry techniques of sufficientspecificity, sensitivity and precision.

The third phase of the method according to the present invention is todetermine the relative levels of the two selected analysed substances,based on the analysis results.

The determination of the extraction ratio of the first substance to thesecond substance may be made either by calculating the ratio of thecollected amount of the first extracted substance in a predeterminedperiod of time to the collected amount of the second extracted substancein the same predetermined period of time, in particular when the firstsubstance and the second substance are extracted simultaneously, or inany case, by first calculating the flux of the first extracted substanceand of the second substance, based on the extracted amounts of the firstsubstance and of the second substance, respectively, and then bycalculating the ratio of the flux of the first extracted substance tothe flux of the second extracted substance.

It should be noted that, in the present invention, since a number ofsubstances are extracted due to the non-selectivity of the iontophoreticextraction, more than two substances may be analysed to determine theirextracted amount; thus, one iontophoretic extraction allows thedetermination of the extraction ratio of two substances for more thanone pair of extracted substances.

Thus, according to the present invention, if more than two substancesare analysed, multiple extraction ratios may be determined.

In one embodiment, the ratio of the extracted amounts or the ratio ofthe extracted fluxes of the first substance A (Qa) and the secondsubstance B (Qb) directly reflects their relative concentrations in thebiological system ([A]/[B]), i.e.,Qa/Qb=K·{[A]/[B]}  (equation 1)where K is a constant.

This embodiment is advantageous when the ratio of A to B in thebiological system is indicative, for example, of the development of aparticular pathological state. It follows that a change in Qa/Qbdirectly reflects the same relative change in the ratio [A]/[B] in thebiological system.

In a second embodiment, when substance B is selected so that, in apopulation, [B] is invariant, a change in Qa/Qb directly reflects thecorresponding change in [A].

In other words,Qa/Qb=K′·[A]  (equation 2)where K′(=K([B]) is a constant.

This embodiment is advantageous when it is known that a change in thevalue of [A] by a certain percentage, up or down, poses a medical risk(e.g., a drug level too low for effect or too high and potentiallytoxic), or indicates a need for alternative therapeutic intervention.

In another embodiment, equations (1) and (2) are particularly usefulwhen substance B is selected so that, in a population, [B] is invariantand can be considered constant, and K (and hence K′) is known.

In this case, the measured ratio Qa/Qb can be directly converted intothe concentration of A ([A]) in the biological system, without the needto calibrate with a blood sample.

Examples of couples of analyte/internal standard which may be applied inthe present invention are lithium/potassium, lithium/sodium,lactate/chloride, lactate/sodium, lactate/potassium, glucose/sodium,glucose/potassium, ammonium/sodium, ammonium/potassium,potassium/sodium, ethanol/sodium, ethanol/potassium, valproate/chloride,valproate/potassium, valproate/sodium, these examples of course notbeing limited to these couples.

Certain examples below will show how substance B may be selected and howK (and hence K′) may be determined in order that this embodiment bepractical.

The present invention also provides a iontophoretic sampling device fornon-invasively monitoring the relative levels of two substances presentin a biological system, this device being conceived to provideinformation on the relative levels of two substances or preferablyinformation on the physiological level of one substance to a patient whowould wear the device at a convenient location, such as the wrist.

The iontophoretic sampling device according the present inventionapplies the method according to the present invention so that the abovedescription in relation with the method may be considered in a generalmanner for the device.

The iontophoretic sampling device according to the present inventioncomprises, as for the iontophoretic device represented schematically inFIG. 1, an electrical power supply, a collection assembly comprising afirst collection chamber containing a first electroconductive medium incontact with a first electrode and a second collection chambercontaining a second electroconductive medium in contact with a secondelectrode, said electrodes being reversible electrodes, preferablysilver/silver chloride electrodes, and being each in contact with theelectrical power supply when the collection assembly is inserted in theiontophoretic device.

Further, this device according to the present invention comprises ameans for analysing automatically two or more selected charged and/oruncharged substances in either one or both of the collection chambers inorder to determine their extracted amounts.

For example, the means of analysing both the selected substances mayinvolve specific enzymes, ion-selective chemistry, measurement ofconductivity and all other known analytical chemistry techniques ofsufficient specificity, sensitivity and precision.

Further, the device according the present invention comprises a meansfor converting the extracted amounts of a first substance and a secondsubstance to the extraction ratio of the first substance to the secondsubstance, wherein said first and second substances are selected in sucha way that the transport and/or transference number of the firstsubstance is independent of the transport and/or transference number ofthe second substance.

According to an embodiment, the means for converting the extractedamounts of a first substance and a second substances to the extractionratio of the first substance to the second substance is a programmablemeans able to calculate the ratio of the collected amount of the firstextracted substance to the collected amount of the second extractedsubstance.

In another embodiment, the means for converting the extracted amounts ofa first substance and a second substance to the extraction ratio of thefirst substance to the second substance is a programmable means able tofirst calculate the fluxes of the first extracted substance and of thesecond substance, based on the extracted amounts of the first substanceand of the second substance, respectively, and then to calculate theratio of the flux of the first extracted substance to the flux of thesecond extracted substance.

The iontophoretic sampling device according to the present invention maybe conceived to provide information on the relative levels of the firstsubstance to the second substance when the first and second substancesfor which the extraction ratio is to be determined are susceptible tochanges in their concentration in the biological system.

Further, the iontophoretic sampling device according to the presentinvention may be conceived to provide information on physiologicalconcentration of the first substance when the first substance issusceptible to changes in its concentration in the biological system andthe second substance has a substantially constant concentration in thebiological system, the physiological concentration of the firstsubstance being determined based upon the constant physiologicalconcentration of the second substance.

The iontophoretic device according to the present invention may furthercomprise a means to reverse the electrode polarity subsequent to eachextraction/analysis cycle.

In a particularly preferred embodiment, the iontophoretic samplingdevice according the present invention is miniaturised to be worn on aperson's body.

Such a miniaturised form may be, for example, conceived to be worn onthe wrist by a patient.

Such a miniaturised device may be used for example to monitor thephysiological level of glucose present in diabetic patient, without acalibration based on a blood sampling, since the physiologicalconcentration of the glucose would be determined based upon the constantphysiological concentration of a second substance, for example sodiumion, acting as an internal standard.

The invention will be now further explained in more detail with thefollowing Examples referring to FIGS. 3-25.

EXAMPLES Example 1

A series of in vitro experiments was performed in specifically-designediontophoresis diffusion cells (Laboratory Glass Apparatus, Berkeley,Calif., USA) as represented in FIG. 3.

The sub-dermal (donor) solution was a pH 7.4 buffer (25 mM Hepes+133 mMNaCl) to which 60 μM glutamate was added as an internal standard.

The analyte of interest was the anti-epileptic drug valproate, which wasincluded at 4 different concentrations: 21 μM, 35 μM, 70 μM and 104.5μM.

To facilitate the analytical chemistry, the donor solution was spikedwith tritiated valproate and with ¹⁴C-labeled glutamate.

The anodal and cathodal chambers contacted the outer surface of the skinand contained the receptor (collection) media, respectively, 75 mMNaCl+25 mM Hepes and 133 mM NaCl+25 mM Hepes (both buffered at pH 7.4).

Full-thickness pig-ear skin was clamped between the two halves of theiontophoresis cell and each chamber filled with the appropriatesolution.

A schema of the experiment is shown in FIG. 3.

A current of 0.4 mA (0.5 mA/cm²) was passed between silver-silverchloride, (Ag/AgCl) electrodes, inserted into the anodal and cathodalchambers, for a total of 5 hours.

Every hour, the entire content of the anode solution was withdrawn andthe chamber refilled with fresh buffer.

The cathodal chamber was sampled only at the end of 5 hours of currentpassage.

Subsequent to this first period of 5 hours at 0.4 mA, a reduced currentof 0.1 mA was passed for the next 19 hours, at the end of which bothanodal and cathodal chambers were sampled.

The total experiment therefore lasted 24 hours.

All samples were analyzed for glutamate and valproate by liquidscintillation counting.

At least 6 replicates were performed for each valproate concentration.

The results showed, as expected, that both valproate and glutamate(which are negatively charged) were extracted at the anode.

Table I shows the extraction flux of both anions for each sampling timeand for each valproate concentration.

FIGS. 4 a-b present the results measured at 5 and 24 hours.

Valproate extraction fluxes increased with concentration, while the fluxof glutamate remained the same for all experiments and was independentof valproate concentration.

TABLE I Extraction fluxes (pmoles · h⁻¹ · cm⁻²) of valproate andglutamate for each sampling period. Glutamate concentration was always60 μM. The current was 0.4 mA during the first 5 hours and 0.1 mA duringthe next 19 hours. Values are given as mean (±standard deviation).[Valproate] = [Valproate] = [Valproate] = [Valproate] = 21 μM 35 μM 70μM 104.5 μM Valproate Glutamate Valproate Glutamate Valproate GlutamateValproate Glutamate Time (h) flux flux flux flux flux flux flux flux 0-118 118  42 155  53  88 120 148 (±12)  (±67) (±19) (±82) (±29) (±45)(±65) (±63) 1-2 50 308 113 367 185 267 313 361 (±17)  (±118)  (±32)(±87) (±83) (±103)  (±100)  (±71) 2-3 79 440 161 484 268 388 440 490(±22)  (±110)  (±40) (±85) (±99) (±94) (±108)  (±54) 3-4 92 479 202 571342 494 531 566 (31) (±86) (±50) (±42) (±114)  (±102)  (±128)  (±74) 4-5112  570 220 588 369 524 600 599 (±30)  (±77) (±47) (±49) (±106)  (±82)(±108)  (±77)  5-24 41 142  82 143 160 146 228 157 (±4) (±23) (±17)(±16) (±25) (±24) (±33) (±23)

Table II and FIGS. 5 a-b show the transport numbers of valproate andglutamate calculated at the 4-5^(th) hours of current passage (0.4 mA)and at the 5-24th hours (0.1 mA).

From each individual cell, and at each sampling point, the ratio[extracted valproate/extracted glutamate] was obtained.

The means and standard deviations of these ratios are collected in TableIII.

FIG. 6 a shows the linear correlation between the extraction ratio(valproate/glutamate) and the valproate concentration in the sub-dermalsolution.

FIG. 6 b shows the linear correlation between the extracted ratio of theanions and their molar ratio (valproate/glutamate) in the sub-dermalsolution.

TABLE II Transport numbers (×10⁶) of valproate and glutamate determinedat each sampling period. Time [Valproate] = 21 μM [Valproate] = 35 μM[Valproate] = 70 μM [Valproate] = 104.5 μM (h) Valproate GlutamateValproate Glutamate Valproate Glutamate Valproate Glutamate 0-1 1.20 ±0.79 7.89 ± 4.51 2.23 ± 5.47 10.4 ± 5.47 3.56 ± 1.96 5.92 ± 3.03 8.04 ±4.37 9.92 ± 4.20 1-2 3.38 ± 1.13 20.6 ± 7.92 7.60 ± 2.14 24.6 ± 5.8312.4 ± 5.57 17.9 ± 6.88 21.0 ± 6.68 24.2 ± 4.79 2-3 5.26 ± 1.48 29.5 ±7.38 10.8 ± 2.70 32.4 ± 5.71 18.0 ± 6.65 26.0 ± 6.32 29.5 ± 7.21 32.8 ±3.60 3-4 6.15 ± 2.11 32.1 ± 5.77 13.5 ± 3.38 38.2 ± 2.84 22.9 ± 7.6133.1 ± 6.80 35.6 ± 8.56 37.9 ± 4.98 4-5 7.48 ± 2.01 38.2 ± 5.19 14.8 ±3.15 39.4 ± 3.28 24.7 ± 7.09 35.1 ± 5.52 40.2 ± 7.22 40.1 ± 5.16  5-2410.9 ± 1.20 38.1 ± 6.24 22.0 ± 4.66 38.3 ± 4.24 42.9 ± 6.74 39.2 ± 6.4561.0 ± 8.81 42.2 ± 6.22

TABLE III Ratio of [valproate/glutamate] extraction fluxes as a functionof time of sampling and as a function of subdermal valproateconcentration. Subdermal glutamate concentration was always 60 μM. Thecurrent was 0.4 mA during the first 5 hours and 0.1 mA during the next19 hours. Subdermal V/G is the ratio of valproate to glutamateconcentrations in the donor, sub-dermal solution. Values are mean ±standard deviation. [Valproate] = 20.98 μM [Valproate] = 34.96 μM[Valproate] = 69.93 μM [Valproate] = 104.5 μM Time (h) Subdermal V/G =0.35 Subdermal V/G = 0.58 Subdermal V/G = 1.16 Subdermal V/G = 1.74 0-10.17 ± 0.05 0.29 ± 0.08 0.59 ± 0.11 0.83 ± 0.25 1-2 0.17 ± 0.03 0.32 ±0.09 0.68 ± 0.15 0.88 ± 0.25 2-3 0.18 ± 0.03 0.34 ± 0.09 0.68 ± 0.170.91 ± 0.23 3-4 0.19 ± 0.04 0.35 ± 0.09 0.68 ± 0.17 0.94 ± 0.21 4-5 0.20± 0.06 0.37 ± 0.08 0.70 ± 0.17 1.01 ± 0.19  5-24 0.29 ± 0.04 0.58 ± 0.151.10 ± 0.12 1.46 ± 0.22

To illustrate how this technique would work in practice, consider somepractical situations using the information and relationships obtainedfrom the experiments described above.

Consider a patient taking valproic acid, whose plasma glutamateconcentration is 60 μM, and on whom a reverse iontophoretic procedure isperformed.

Suppose that analysis of the extracted samples indicate that 741 pmolesof glutamate and 724 pmoles of valproate are extracted in 1 hour(4-5^(th) hours of extraction).

The extracted ratio (valproate/glutamate) is 0.977.

Now this information could be used in different ways:

-   [a] Assume a therapeutic range for valproate of 3-10 mg/L (or 21 to    69 μM) of the free drug.

Such values correspond to molar ratios (valproate/glutamate) of 0.35 and1.15 in the sub-dermal fluids.

According to our in vitro results (by substitution in the regressionequation obtained at 5 hours, FIGS. 6 a-b), an extraction ratio of 0.977indicates that the valproate concentration systemically is 100 μM (FIG.6 a), i.e., the sub-dermal [valproate]/[glutamate] ratio is 1.67 (FIG. 6b).

We would conclude, therefore, that the valproate plasma levels of thispatient were too high and out of the therapeutic range.

In fact, the values assumed for this hypothetical patient correspond toone of our in vitro experiments with a sub-dermal valproateconcentration of 104.5 μM and a [valproate]/[glutamate] ratio of 1.74.

In other words, there is a good predictive value of the equationsdeveloped.

-   [b] For the molar sub-dermal ratios of 0.35 and 1.15 (low and high    limits of the therapeutic window), iontophoresis extraction ratios    of 0.21 and 0.68, respectively, can be deduced.

These are exactly the values predicted by the regression equation inFIG. 6 b and we can therefore translate “real” plasma values, whichdelimit the therapeutic range, into extracted iontophoretic ratios.

We can now conclude that the plasma levels of valproate obtained fromthis patient are outside the therapeutic window: the extraction ratio of0.977, falls well beyond the limits of 0.21 and 0.68.

This second approach can also be used for any situation in which therelative concentration of two markers (of clinical, therapeutic, toxiceffect, etc.) is of relevance and interest.

It is important to note that the data of the example above correspond toone of the in vitro replicates in which the donor valproateconcentration was held at 104.5 μM.

On the other hand, the regression equations used for the calculationwere derived from many experiments performed with pig ear skin obtainedfrom several different donors.

This supports our hypothesis that inter and intra-individual variabilityaffects glutamate and valproate extraction in the same way.

It is further important to reiterate that FIGS. 6 a-b demonstrate thedetermination of the constants K and K′ necessary to calculate anabsolute concentration of an analyte in the biological system from theextracted ratio of the analyte to the chosen internal standard.

In this example, the chosen analyte (A) is valproate, while the internalstandard (B) is glutamate.

According to Equation 1, therefore,Qval/Qglu=K.[val]/[glu]

K is the slope of the graph in FIG. 6 b; that is, following a short(5-hour) period of iontophoresis at 0.5 mA/cm², K=0.57.

On the other hand, following a longer (19-hour) period of iontophoresisat 0.1 mA/cm², K=0.83.

Similarly, according to Equation 2,Qval/Qglu=K′.[val]

K′ is the slope of the graph in FIG. 6 a and is equal to K divided bythe fixed glutamate concentration (60 μM) in the biological system.

Following a short (5-hour) period of iontophoresis at 0.5 mA/cm²,K′=0.0096

On the other hand, following a longer (19-hour) period of iontophoresisat 0.1 mA/cm², K′=0.0138.

It follows that, once the value of K′ has been established for aparticular pair of substances, and given that the concentration of theinternal standard ([B]) in the biological system is constant, thenEquation 2 can be used to determine the concentration of the analyte ofinterest ([A]) directly from the iontophoretic extraction ratio Qa/Qb.

Example 2

Experiments were performed in specially-designed iontophoresis diffusioncells (Laboratory Glass Apparatus, Berkeley, Calif., USA) as representedin FIG. 7.

The sub-dermal (donor) solution was a pH 7.4 buffer (25 mM Tris+34 mMMops+130 mM NaCl+4 mM KCl), in which potassium, sodium and chloride ionsacted as the internal standards.

The two analytes of interest were lactate (negatively charged) andammonium (positively charged).

In a first experiment, lactate and ammonium concentrations sub-dermallywere 1.74 mM and 1.56 mM.

In a second experiment, lactate and ammonium concentrations were 0.73 mMand 0.78 mM.

The anodal and cathodal chambers contacted the outer surface of the skinand contained the receptor (collection) media, respectively, 80 mMTris/TrisHCl and 25 mM Tris+34 mM Mops (both buffered to pH 7.4).

Dermatomed pig-ear skin was clamped between the two halves of theiontophoresis cell and each chamber was filled with the appropriatesolution.

A schema of the experiment is shown in FIG. 7.

The sub-dermal chamber was filled with the “donor” solution which wasperfused continuously at 2-3 mL/hour by means of a peristaltic pump.

A current of 0.4 mA (0.5 mA/cm²) was passed for a total of 5 hoursbetween the Ag/AgCl electrodes which were inserted into the anodal andcathodal chambers.

Every hour, the entire anode and cathode solutions were withdrawn andthe chambers were refilled with fresh buffer.

All the samples were analyzed for lactate, ammonium, potassium, sodiumand chloride.

As expected, the positively-charged ammonium, potassium and sodiumcations were collected at the cathodal (negative) electrode, while thenegatively-charged lactate and chloride anions were collected at thepositive electrode (anode).

Table IV and FIGS. 8 a-b show the extraction fluxes for these 5 speciesat the 3^(rd) and 5^(th) hours of the experiment.

Lactate and ammonium fluxes changed in proportion with their sub-dermalconcentrations while the fluxes of potassium, chloride and sodiumremained essentially constant.

TABLE IV Extraction fluxes for Na⁺, K⁺ and ammonium⁺ at the cathode andfor lactate⁻ and chloride⁻ at the anode. Values are mean ± standarddeviation. Ammonium Lactate K⁺ Na⁺ Cl⁻ (nmoles · (nmoles · (nmoles ·(nmoles · (nmoles · Analyte concentrations^(a) Time (h) h⁻¹ · cm⁻²) h⁻¹· cm⁻²) h⁻¹ · cm⁻²) h⁻¹ · cm⁻²) h⁻¹ · cm⁻²) [lactate] = 1.74 mM 3 260 ±17 113 ± 15 760 ± 90 12960 ± 1530 9430 ± 0   [ammonium] = 1.56 mM 5 275± 5  107 ± 13 780 ± 10 13790 ± 210  7850 ± 830  [lactate] = 0.73 mM 3145 ± 18 45 ± 8 900 ± 27 13620 ± 218  5510 ± 1150 [ammonium] = 0.78 mM 5140 ± 11  43 ± 10 820 ± 21 12460 ± 1540 7670 ± 1480 ^(a)Sub-dermalconcentrations of K⁺, Na⁺ and Cl⁻ were always 4 mM, 133 mM and 137 mMrespectively.

Table V and FIGS. 9 a-b present the transport numbers of the twoanalytes of interest (lactate and ammonium) and of the three internalstandards (K⁺, Na⁺ and Cl⁻) considered.

For each individual cell and at each sampling time the following ratiosof extracted ions were determined: [a] (ammonium/sodium), [b] (ammonium/potassium), [c] (lactate/chloride), [d] (lactate/sodium), [e](lactate/potassium), and [f] (potassium/sodium).

The means and standard deviations of these ratios are shown in Table VIand FIGS. 10 a-b.

These values in turn can be used to determine K and K′ for eachanalyte/internal standard couple, as described in the preceding example.

The values of K are in Table VII below.

Values of K′ can be obtained simply by dividing K by the appropriateconcentration in the biological system of the applicable internalstandard.

TABLE V Deduced analyte and internal standard transport numbers (×100).Values are mean ± standard deviation. Analyte concentrations Time (h)Ammonium Lactate K⁺ Na⁺ Cl⁻ [lactate] = 1.74 mM 3 1.36 ± 0.09 0.59 ±0.08 3.99 ± 0.45 67.72 ± 7.98 57.68 ± 0.00 [ammonium] = 1.56 mM 5 1.44 ±0.03 0.56 ± 0.07 4.06 ± 0.05 72.07 ± 1.07 50.69 ± 5.36 [lactate] = 0.73mM 3 0.76 ± 0.09 0.24 ± 0.04 4.72 ± 1.40  71.17 ± 11.40 38.40 ± 8.04[ammonium] = 0.78 mM 5 0.73 ± 0.06 0.23 ± 0.05 4.26 ± 1.08 65.14 ± 8.07 52.47 ± 10.12

TABLE VI Extracted flux ratios (×10³) of analytes and internalstandards. Values are mean ± standard deviation. Time Analyteconcentrations (h) NH₄ ⁺/Na⁺ NH₄ ⁺/K⁺ Lactate⁻/Na⁺ Lactate⁻/K⁺Lactate⁻/Cl⁻ K⁺/Na⁺ Subdermal Ratio (·10³) 11.7 390 13.1 435 12.6 30[lactate] = 1.74 mM 3 20 ± 1.1 342 ± 16 8.7 ± 0.1  149 ± 3.3   12 ± 1.659 ± 0.3 [ammonium] = 1.56 mM 5 20 ± 0.1 354 ± 11 7.8 ± 1.1 138 ± 15  14 ± 3.2 56 ± 1.6 Subdermal Ratio (·10³)  5.8 195  5.4 181  5.2 30[lactate] = 0.73 mM 3 11 ± 1.0 166 ± 24 3.3 ± 0.6 52 ± 16 7.8 ± 1.0 66 ±9.5 [ammomium] = 0.78 mM 5 11 ± 0.8 178 ± 29 3.5 ± 0.9 55 ± 19 6.0 ± 2.865 ± 8.7

TABLE VII Values of K determined for each analyte/internal standardcouple from the data in Table VI. Analyte concentrations Time (h) NH₄⁺/Na⁺ NH₄ ⁺/K⁺ Lactate⁻/Na⁺ Lactate⁻/K⁺ Lactate⁻/Cl⁻ K⁺/Na⁺ SubdermalRatio (·10³) 11.7 390 13.1 435 12.6 30 [lactate] = 1.74 mM 3 1.71 ± 0.090.88 ± 0.04 0.66 ± 0.01 0.34 ± 0.01 0.95 ± 0.13 1.97 ± 0.01 [ammonium] =1.56 mM 5 1.71 ± 0.01 0.91 ± 0.03 0.60 ± 0.08 0.32 ± 0.03 1.11 ± 0.251.87 ± 0.05 Subdermal Ratio (·10³)  5.8 195  5.4 181  5.2 30 [lactate] =0.73 mM 3 1.90 ± 0.09 0.85 ± 0.12 0.61 ± 0.11 0.29 ± 0.09 1.50 ± 0.192.20 ± 0.32 [ammomium] = 0.78 mM 5 1.90 ± 0.14 0.91 ± 0.15 0.65 ± 0.170.30 ± 0.10 1.15 ± 0.54 2.17 ± 0.29

It is clear that the data obtained in these experiments may be used asdescribed in the first example to estimate whether the sub-dermalconcentration of the analyte of interest falls within or outside anacceptable limit.

The use of more than one internal standard demonstrates the generalityof the approach and offers a means to improve the precision, safety andaccuracy of the method.

The consistency of the extraction ratio of internal standards acts as afurther safety check, in that it permits the constancy of theirsub-dermal levels (which is an assumed requirement) to be verifiedsimply.

We also note that, despite the fact that lactate and Na⁺ are collectedat opposite electrodes, their extraction flux ratio is also a reflectionof, and proportional to, the ratio of their sub-dermal concentrations.

This indicates that it is not always necessary to use, as an internalstandard, a species which is extracted to the same electrode as theanalyte of interest.

This may be important when assay methods interfere with one another, forexample.

Lastly, the data in this example demonstrate that multiple analytes maybe extracted and detected in a single reverse iontophoresis procedureand that the transport of each can be referenced to that of anappropriate “internal standard”.

Example 3

Dermatomed pig-ear skin was clamped between the two halves ofside-by-side diffusion cells (area=0.78 cm²) as represented in FIG. 11.

The anode was placed in the sub-dermal, “donor” chamber, which containeda physiological pH 7.4 buffer (25 mM Tris/TrisHCl+133 mM NaCl) to whichthe analyte mannitol was added.

Mannitol is a non-metabolizable sugar with properties (includingmolecular weight and lipophilicity) very similar to glucose.

In a first experiment, mannitol concentration was 5 mM for the firstthree hours of experiment and was then increased to 10 mM for asubsequent period of three hours.

To facilitate the analytical chemistry, the donor solutions were spikedwith ¹⁴C-labeled mannitol.

Sodium ion was the chosen internal standard.

The cathodal (collection) chamber, which contacted the outer surface ofthe skin contained a 25 mM Tris/TrisHCl buffer at pH 7.4.

A schema of the experiment is shown in FIG. 11.

A current of 0.4 mA (0.5 mA/cm²) was passed between the Ag/AgClelectrodes for a total of 6 hours.

During the first 3-hour period, the entire content of the cathodesolution was withdrawn every 60 minutes and the chamber was refilledwith fresh buffer.

During the second 3-hour period, the 5 mM mannitol donor solution wasreplaced with 10 mM mannitol, and the cathodal chamber was then sampledevery 30 minutes.

Mannitol and sodium ions in each sample were quantified by liquidscintillation counting and by an ion specific electrode, respectively.

FIG. 12 and Table VIII show the fluxes of mannitol and sodium over thesix hours of experiment.

The data show that the mannitol flux changed abruptly when itsconcentration in the sub-dermal solution was increased from 5 to 10 mM.

On the other hand, the sodium flux reached a constant value thatremained invariable over the entire course of the experiment.

FIG. 13 and Table VIII show the correlation between the iontophoreticextraction ratio of mannitol to sodium and their sub-dermalconcentration ratio over the six-hours period of the experiment.

TABLE VIII Extraction fluxes and extracted flux ratios (×10³) formannitol and Na⁺. Values are mean ± standard deviation. SubdermalMannitol flux Sodium⁺ flux Extracted [Mannitol] [mannitol/Na⁺] (nmol ·(μmol · (mannitol/Na⁺) Time (min) (mM) (×10³) ratio h⁻¹ · cm⁻²) h⁻¹ ·cm⁻²) flux (×10³) ratio 60 5 37.6 13.3 ± 7.6  7.9 ± 0.5 1.7 ± 0.8 12021.0 ± 4.7  9.7 ± 0.6 2.2 ± 0.3 180 25.2 ± 4.3 10.1 ± 0.4 2.5 ± 0.3 21010 75.2 52.2 ± 4.4 10.3 ± 0.5 5.0 ± 0.2 240 53.2 ± 7.7 10.4 ± 0.6 5.1 ±0.5 270 54.1 ± 6.8 10.3 ± 0.4 5.2 ± 0.5 300 58.1 ± 4.5 10.6 ± 0.3 5.5 ±0.3 330 60.9 ± 6.8 10.7 ± 0.3 5.7 ± 0.4 360 63.2 ± 6.2 10.5 ± 0.6 6.0 ±0.3

In a second experiment, performed under identical conditions to thefirst (see FIG. 11), mannitol concentration was 5 mM for the first threehours of experiment, it was then reduced to 3 mM for a subsequent periodof one hour and then increased to 10 mM for a subsequent period of onehour.

Sodium ion was again the chosen internal standard.

A current of 0.4 mA (0.5 mA/cm²) was passed between the Ag/AgClelectrodes for a total of 5 hours.

During the first 3-hour period, the entire content of the cathodesolution was withdrawn every 60 minutes and the chamber was refilledwith fresh buffer.

During the second 1-hour period, the 5 mM mannitol donor solution wasreplaced with 3 mM mannitol, and the cathodal chamber was then sampledevery 30 minutes.

During the third 1-hour period, the 3 mM mannitol donor solution wasreplaced with 10 mM mannitol, and the cathodal chamber was then sampledevery 30 minutes.

Mannitol and sodium ions in each sample were again quantified by liquidscintillation counting and by an ion specific electrode, respectively.

FIGS. 14 a-b and Table IX show the fluxes of mannitol and sodium andalso the (mannitol/sodium) extraction flux ratio over the 5 hours ofexperiment.

TABLE IX Extraction fluxes and extracted flux ratios (×10³) for mannitoland Na⁺. Values are mean ± standard deviation. Subdermal Mannitol fluxSodium⁺ flux Extracted [Mannitol] [mannitol/Na⁺] (nmol · (μmol ·(mannitol/Na⁺) Time (min) (mM) (×10³) ratio h⁻¹ · cm⁻²) h⁻¹ · cm⁻²) flux(×10³) ratio 60 5 37.6 13.5 ± 4.1 8.8 ± 0.7 1.52 ± 0.4  120 25.8 ± 4.810.2 ± 0.7  2.5 ± 0.3 180 27.8 ± 4.4 10.4 ± 0.7  2.7 ± 0.3 210 3 22.516.6 ± 3.2 10.9 ± 0.7  1.5 ± 0.2 240 14.1 ± 2.8 9.7 ± 0.5 1.5 ± 0.5 27010 75.2 49.6 ± 8.4 9.4 ± 0.6 5.2 ± 0.5 300 48.1 ± 8.7 9.3 ± 0.4 5.2 ±0.7

The data show that the mannitol flux nearly halved when itsconcentration in the sub-dermal solution was decreased from 5 to 3 mMand then increased abruptly when the sub-dermal solution was increasedfrom 3 to 10 mM.

On the other hand, the sodium flux reached a constant value thatremained invariable over the entire course of the experiment.

FIGS. 15 a-b show the correlation between the iontophoretic extractionratio of mannitol to sodium and [a] the mannitol sub-dermalconcentration, and [b] the sub-dermal concentration ratio(mannitol/sodium) over the 5-hour period of the experiment.

The two experiments in this example clearly show that the reverseiontophoretic extraction of a neutral molecule (mannitol) byelectroosmosis can be “calibrated” by the use of an ionic internalstandard (Na⁺) which moves across the skin by electromigration.

The molecular similarity between mannitol and glucose implies that thesame approach can be used for glucose monitoring, as will demonstratedin a subsequent example.

To illustrate how this technique would work in practice, consider somepractical situations using the information and relationships obtainedfrom the experiments described above.

Consider a hypothetical patient, whose NaCl concentration in plasma is133 mM, on whom a reverse iontophoretic procedure is performed.

Suppose that analysis of the extracted samples indicates that 14.26nmoles of mannitol and 10.14 μmoles of sodium are extracted across 1 cm²of skin in 1 hour.

The extracted ratio (mannitol/sodium) is 1.4×10⁻³.

Now this information could be used in different ways:

-   [a] Assume, in this hypothetical patient, that the “normal”    concentration range of mannitol is 80-100 mg/dL (or 4.4 to 5.5 mM).

Such values correspond to molar ratios (mannitol/sodium) of 33×10⁻³ and41×10⁻³ in the sub-dermal fluids, assuming a constant sodiumconcentration of 133 mM.

According to our in vitro results (by substitution in the regressionequation of FIG. 15 a), an extraction ratio of 1.4×13 indicates that themannitol concentration systemically is 2.8 mM, i.e., the sub-dermal[mannitol]/[sodium] ratio is 20.7×10⁻³ (FIG. 15 b).

We would conclude, therefore, that the mannitol plasma levels of thispatient were too low.

In fact, the values assumed for this hypothetical patient correspond toone of our in vitro experiments with a sub-dermal mannitol concentrationof 3 mM and a [mannitol]/[sodium] ratio of 22.5×10⁻³.

In other words, there is a good predictive value of the equationsdeveloped.

-   [b] For the molar sub-dermal ratios of 33×10⁻³ and 41×10⁻³ (low and    high limits of the “hypothetical” normal range of mannitol),    iontophoresis extraction ratios of 2.26×10⁻³ and 2.82×10⁻³,    respectively, can be deduced.

These are exactly the values predicted by the regression equation inFIG. 15 b and we can therefore translate “real” plasma values, whichdelimit the acceptable range, into extracted iontophoretic ratios.

We can now conclude that the plasma levels of mannitol obtained fromthis patient are outside the normal range: the extraction ratio of1.4×10⁻³, falls well beyond the limits of 2.26×10⁻³ and 2.82×10⁻³.

It is further important to reiterate that FIGS. 15 a-b demonstrate thedetermination of the constants K and K′ necessary to calculate anabsolute concentration of an analyte in the biological system from theextracted ratio of the analyte to the chosen internal standard.

In this example, the chosen analyte (A) is mannitol, while the internalstandard (B) is Na⁺.

According to Equation 1, therefore,Qmann/QNa⁺ =K.[mann]/[Na⁺]

K can be read from the slope of the graph in FIG. 15 b; that is,following periods of iontophoresis of between 3 and 5 hours at 0.5mA/cm², K=0.07.

Similarly, according to Equation 2,Qmann/QNa⁺ =K′.[mann]

K′ can be read from the slope of the graph in FIG. 15 a and is equal toK divided by the fixed Na⁺ concentration (133 mM) in the biologicalsystem.

Following periods of iontophoresis of between 3 and 5 hours at 0.5mA/cm², K′=0.525×10⁻³.

It follows that, once the value of K′ has been established for aparticular pair of substances, and given that the concentration of theinternal standard ([B]) in the biological system is constant, thenEquation 2 can be used to determine the concentration of the analyte ofinterest ([A]) directly from the iontophoretic extraction ratio Qa/Qb.

Example 4

Dermatomed pig-ear skin was clamped between the two halves ofside-by-side diffusion cells (area=0.78 cm²).

The anode was placed in the sub-dermal, “donor” chamber, which containeda physiological pH 7.4 buffer (25 mM Tris/TrisHCl+4 mM KCl).

The analyte of interest was mannitol and sodium ion was the choseninternal standard.

Both the concentration of the analyte of interest and the internalstandard were modified during the experiment.

Sodium and mannitol concentrations were 133 and 5 mM, respectively, forthe first three hours.

Then, sodium and mannitol concentrations were changed to 125 and 10 mM,respectively, for a subsequent period of one hour.

Then, sodium and mannitol concentrations were changed to 145 and 3 mM,respectively, for a subsequent period of one hour.

Finally, sodium and mannitol concentrations were changed to 133 and 5mM, respectively, for the last hour of the experiment.

The range of sodium concentrations chosen corresponds to that which canoccur normally in human subjects.

In other words, there will almost always be some slight variation in theconcentration of an internal standard in the biological system.

The objective of this experiment was to test, therefore, whether suchtypical variability would impact significantly on the results deducedfrom a reverse iontophoresis procedure based on the invention disclosed.

To facilitate the analytical chemistry, the donor solutions were spikedwith ¹⁴C-labeled mannitol.

The cathodal (collection) chamber, which contacted the outer surface ofthe skin, contained a 25 mM Tris/TrisHCl buffer at pH 7.4.

A schema of the experiment is shown in FIG. 16.

A current of 0.4 mA (0.5 mA/cm²) was passed between the Ag/AgClelectrodes for a total of 6 hours.

During the first 3-hour period, the entire content of the cathodesolution was withdrawn every 60 minutes and the chamber was refilledwith fresh buffer.

During the second 1-hour period, the 5 mM mannitol/133 mM NaCl donorsolution was replaced with 10 mM mannitol/125 mM NaCl, and the cathodalchamber was then sampled every 30 minutes.

During the third 1-hour period, the donor solution was replaced with 3mM mannitol/145 mM NaCl, and the cathodal chamber was then sampled every30 minutes.

During the final 1-hour period, the donor solution was replaced with 5mM mannitol/133 mM NaCl, and the cathodal chamber was then sampled every30 minutes.

Mannitol and sodium ions in each sample were quantified by liquidscintillation counting and by an ion specific electrode, respectively.

FIGS. 17 a-b and Table X show the extraction fluxes and also the(mannitol/sodium) extraction flux ratio over the 6 hours of experiment.

TABLE X Extraction fluxes and extracted flux ratios (×10³) for mannitoland Na⁺. Values are mean ± standard deviation. Subdermal Mannitol fluxSodium⁺ flux Extracted [Mannitol]/[Na⁺] [mannitol/Na⁺] (nmol · (μmol ·(mannitol/Na⁺) Time (min) (mM) (×10³) ratio h⁻¹ · cm⁻²) h⁻¹ · cm⁻²) flux(×10³) ratio 60 5/133 37.6  9.7 ± 1.5  8.4 ± 0.8 1.2 ± 0.2 120 22.0 ±1.6 10.7 ± 0.4 2.1 ± 0.1 180 28.8 ± 1.3 11.0 ± 0.3 2.6 ± 0.1 240 10/125 80 57.7 ± 4.2 11.7 ± 0.3 5.0 ± 0.4 240 52.2 ± 3.3 10.9 ± 0.8 4.9 ± 0.5270 3/145 20.7 15.9 ± 0.7 10.4 ± 0.5 1.6 ± 0.1 300 15.3 ± 0.7 10.7 ± 0.41.4 ± 0.1 330 5/133 37.6 29.0 ± 0.8 11.2 ± 1.2 2.7 ± 0.1 360 29.3 ± 0.611.4 ± 0.3 2.6 ± 0.1

FIG. 18 shows the correlation between the iontophoretic extraction ratioof mannitol to sodium and the mannitol sub-dermal concentration over the6-hour period of the experiment.

This example clearly shows that the reverse iontophoretic extraction ofa neutral molecule (mannitol) by electroosmosis can be “calibrated” bythe use of an ionic internal standard (Na⁺) which moves across the skinby electromigration.

The molecular similarity between mannitol and glucose implies that thesame observations made here would be equally applicable for glucosemonitoring, as will demonstrated in a subsequent example.

Furthermore, this example shows that the method is not undermined bytypical variations in the concentration (in the biological system) ofthe internal standard, in this case sodium ions.

To illustrate how this technique would work in practice, consider somepractical situations using the information and relationships obtainedfrom the experiments described above.

Consider a hypothetical patient on whom a reverse iontophoreticprocedure is performed.

Suppose that analysis of the extracted samples indicates that 58 nmolesof mannitol and 11.7 μmoles of sodium are extracted across 1 cm² of skinin 1 hour.

The extracted ratio (mannitol/sodium) is 4.97×10⁻³.

Now this information could be used as follows:

-   [a] Assume, in this hypothetical patient, that the “normal” range    for mannitol of 80-100 mg/dL (or 4.4 to 5.5 mM) and that the    patient's sodium concentration may vary in the interval 125-145 mM.

Thus, in this case, constant levels of the internal standard are notassumed.

According to our in vitro results (by substitution in the regressionequation of FIG. 18 a) an extraction ratio of 4.97×10⁻³ indicates thatthe mannitol concentration systemically is 10 mM, i.e., we wouldconclude, therefore, that the mannitol plasma levels of this patientwere too high

In fact, the values assumed for this hypothetical patient correspond toone of our in vitro experiments with a sub-dermal mannitol concentrationof 10 mM and a [mannitol]/[sodium] ratio of 80×10⁻³.

In other words, there is a good predictive value of the equationsdeveloped.

-   [b] For the low and high limits (4.4 to 5.5 mM) of the    “hypothetical” normal range of mannitol, iontophoresis extraction    ratios of 2.2×10⁻³ and 2.8×10⁻³, respectively, can be deduced.

These are exactly the values predicted by the regression equation inFIG. 18 and we can therefore translate “real” plasma values, whichdelimit the acceptable range, into extracted iontophoretic ratios.

We can now conclude that the plasma levels of mannitol obtained fromthis patient are outside the normal range: the extraction ratio of4.97×10⁻³ falls well beyond the limits of 2.2×10⁻³ and 2.8×10⁻³.

It should be recalled that FIG. 18 can be used to demonstrate thedetermination of the constant K′ necessary to calculate an absoluteconcentration of an analyte in the biological system from the extractedratio of the analyte to the chosen internal standard.

This procedure was described using the data in the preceding example andthe regressions in FIG. 15 a.

Interestingly, the slope of the regression in FIG. 18 is very close tothose in FIG. 15 a.

From FIG. 15 a, K′ is deduced to be 0.525×10⁻³; from FIG. 18,K′=0.487×10⁻³.

In other words, we derive essentially the same calibration parameterfrom the experiments in this example in which the concentration of theinternal standard was allowed to vary over an interval which may beobserved in a typical biological system.

We conclude, therefore, that the approach is robust.

Example 5

Dermatomed pig-ear skin was clamped between the two halves ofside-by-side diffusion cells (area=0.78 cm²).

The anode was placed in the sub-dermal, “donor” chamber, which containeda physiological pH 7.4 buffer (25 mM Tris/TrisHCl+133 mM NaCl) to whichthe analyte glucose was added at a concentration of 10 mM.

To facilitate the analytical chemistry, the donor solutions were spikedwith tritiated glucose.

Sodium ion was the chosen internal standard.

The cathodal (collection) chamber, which contacted the outer surface ofthe skin, contained a 25 mM Tris/TrisHCl buffer at pH 7.4.

The experimental design was identical to that in FIG. 11, with theexception that glucose spiked with tritiated glucose replaced mannitolspiked with ¹⁴C-labeled mannitol.

A current of 0.4 mA (0.5 mA/cm²) was passed between the Ag/AgClelectrodes for a total of 6 hours.

During this period, the entire content of the cathode solution waswithdrawn every 60 minutes and the chamber was refilled with freshbuffer.

Glucose and sodium ions in each sample were quantified by liquidscintillation counting and by an ion specific electrode, respectively.

FIGS. 19 and 20 and Table XI show the fluxes of glucose and sodium andalso the (glucose/sodium) extraction flux ratio over the 6 hours ofexperiment.

TABLE XI Extraction fluxes and extracted flux ratios (×10³) for glucoseand Na⁺. Values are mean ± standard deviation. Subdermal Glucose fluxSodium⁺ flux Extracted [Glucose] [glucose/Na⁺] (nmol · (μmol ·(glucose/Na⁺) Time (min) (mM) (×10³) ratio h⁻¹ · cm⁻²) h⁻¹ · cm⁻²) flux(×10³) ratio 60 10 75.2 24.1 ± 9.8   8.7 ± 0.6 2.7 ± 0.9 120 43.0 ± 12.6 9.8 ± 0.4 4.4 ± 1.1 180 50.1 ± 11.4 10.1 ± 0.3 4.9 ± 1.0 240 51.5 ±10.4 10.0 ± 0.3 5.1 ± 0.9 300 57.3 ± 10.6 10.2 ± 0.3 5.6 ± 0.9 360 60.5± 10.8 10.2 ± 0.3 5.9 ± 0.9

The data are remarkably similar to those obtained in the essentiallyidentical experiment described in Example 3 in which mannitol was usedinstead of glucose.

The comparison is made with the data in the lower half of Table VII, andwith the graphical results in FIGS. 12 and 13 at times after 180minutes.

This example clearly shows that the reverse iontophoretic extraction ofa neutral molecule (glucose) by electroosmosis can be “calibrated” bythe use of an ionic internal standard (Na⁺) which moves across the skinby electromigration.

Further, the results confirm that mannitol is a good model for glucoseand that the method is applicable, therefore, to noninvasive glucosemonitoring applications.

Example 6

Dermatomed pig-ear skin was clamped between the two halves ofside-by-side diffusion cells (area=0.78 cm²).

The anode was placed in the sub-dermal, “donor” chamber, which containeda physiological pH 7.4 buffer (25 mM Tris/TrisHCl+133 mM NaCl) to whichthe analytes glucose and mannitol were both added, in separateexperiments, each of 6 hours duration, at the following concentrations:

-   -   Glucose, 3 mM; mannitol, 7 mM—Experiment A    -   Glucose, 5 mM; mannitol, 5 mM—Experiment B    -   Glucose, 7 mM, mannitol, 3 mM—Experiment C

To facilitate the analytical chemistry, the donor solutions were spikedwith tritiated glucose and ¹⁴C-labeled mannitol.

Sodium ion was the chosen internal standard.

The cathodal (collection) chamber, which contacted the outer surface ofthe skin, contained a 25 mM Tris/TrisHCl buffer at pH 7.4.

The experimental design was identical to that in FIG. 11, with theexception that both tritiated glucose and ¹⁴C-labeled mannitol werepresent in the ‘donor’ anode chamber.

A current of 0.4 mA (0.5 mA/cm²) was passed between the Ag/AgClelectrodes for a total of 6 hours.

During this period, the entire content of the cathode solution waswithdrawn every 60 minutes and the chamber was refilled with freshbuffer.

Glucose and mannitol in each sample were quantified by liquidscintillation counting; sodium was quantified using an ion specificelectrode.

FIGS. 21 a-c show the fluxes of glucose, mannitol and sodium during the6-hour periods of Experiments A, B and C, respectively.

The data show that glucose and mannitol fluxes responded proportionatelyto their sub-dermal concentrations.

The sodium flux was constant, and had the same absolute value, in eachof Experiments A, B and C.

Tables XII, XII and XIV show the (glucose/sodium), (mannitol/sodium) and(glucose/mannitol) extracted flux ratios, in Experiments A, B and C,respectively, over the 6-hour period of these measurements.

TABLE XII Extracted flux ratios when the subdermal concentrations ofglucose (G) and mannitol (M) were 3 mM and 7 mM, respectively(Experiment A, Example 6). Values are mean ± standard deviation. TimeSubdermal concentration ratios Extracted flux ratios (minutes) (10³×)[G]/[Na⁺] (10³×) [M]/[Na⁺] [glucose]/[mannitol] (10³×) G/Na⁺ (10³×)M/Na⁺ G/M 60 22.5 52.6 0.43 0.85 ± 0.13 2.01 ± 0.33 0.42 ± 0.01 120 1.32± 0.09 3.21 ± 0.21 0.41 ± 0.01 180 1.50 ± 0.10 3.64 ± 0.31 0.41 ± 0.01240 1.65 ± 0.09 3.98 ± 0.24 0.41 ± 0.00 300 1.79 ± 0.15 4.29 ± 0.40 0.42± 0.01 360 1.92 ± 0.10 4.65 ± 0.26 0.41 ± 0.00

TABLE XIII Extracted flux ratios when the subdermal concentrations ofglucose (G) and mannitol (M) were 5 mM and 5 mM, respectively(Experiment B, Example 6). Values are mean ± standard deviation. TimeSubdermal concentration ratios Extracted flux ratios (minutes) (10³×)[G]/[Na⁺] (10³×) [M]/[Na⁺] [glucose]/[mannitol] (10³×) G/Na⁺ (10³×)M/Na⁺ G/M 60 37.6 37.6 1.00 1.18 ± 0.54 1.29 ± 0.58 0.91 ± 0.02 120 1.97± 0.46 2.13 ± 0.47 0.92 ± 0.02 180 2.31 ± 0.39 2.53 ± 0.41 0.91 ± 0.03240 2.50 ± 0.34 2.73 ± 0.38 0.92 ± 0.04 300 2.71 ± 0.36 2.98 ± 0.41 0.91± 0.02 360 2.91 ± 0.26 3.15 ± 0.30 0.92 ± 0.01

TABLE XIV Extracted flux ratios when the subdermal concentrations ofglucose (G) and mannitol (M) were 7 mM and 3 mM, respectively(Experiment C, Example 6). Values are mean ± standard deviation. TimeSubdermal concentration ratios Extracted flux ratios (minutes) (10³×)[G]/[Na⁺] (10³×) [M]/[Na⁺] [glucose]/[mannitol] (10³×) G/Na⁺ (10³×)M/Na⁺ G/M 60 52.6 22.5 2.33 1.79 ± 0.90 0.86 ± 0.45 2.09 ± 0.07 120 2.86± 0.87 1.38 ± 0.46 2.09 ± 0.06 180 3.35 ± 0.83 1.62 ± 0.44 2.08 ± 0.07240 3.57 ± 0.71 1.71 ± 0.39 2.11 ± 0.08 300 3.77 ± 0.64 1.83 ± 0.40 2.08± 0.10 360 3.99 ± 0.59 1.94 ± 0.36 2.07 ± 0.08

FIG. 22 a shows the correlations between (a) the iontophoreticextraction ratio of glucose to sodium and the glucose sub-dermalconcentration, and (b) the iontophoretic extraction ratio of mannitol tosodium and the mannitol sub-dermal concentration, following 6 hours ofiontophoresis at 0.5 mA/cm².

FIG. 22 b shows the correlations between (a) the iontophoreticextraction ratio of glucose to sodium and the sub-dermal concentrationratio (glucose/sodium), and (b) the iontophoretic extraction ratio ofmannitol to sodium and the sub-dermal concentration ratio(mannitol/sodium), following 6 hours of iontophoresis at 0.5 mA/cm².

The overlap between the results for glucose and mannitol, presented inFIGS. 22 a-b confirms the fact that mannitol can act as a model for thebehaviour of glucose in reverse iontophoresis.

This point is emphasized in FIG. 22 c which shows the almost perfectcorrelation between the iontophoretic extraction ratio of glucose tomannitol (following 6 hours of iontophoresis at 0.5 mA/cm²) and thesub-dermal concentration ratio (glucose/mannitol).

The slope of the line of regression is close to unity.

Conclusions deduced earlier on the basis of mannitol data, therefore,are likely to be valid for glucose as well.

This example clearly shows that the reverse iontophoretic extraction ofa neutral molecule (glucose) by electroosmosis can be “calibrated” bythe use of an ionic internal standard (Na⁺) which moves across the skinby electromigration.

Further, the results confirm that mannitol is a good model for glucoseand that the method is applicable, therefore, to non-invasive glucosemonitoring applications.

To illustrate how this technique would work in practice, consider somepractical situations using the information and relationships obtainedfrom the experiments described above.

Consider a hypothetical patient, whose NaCl concentration in plasma is133 mM, on whom a reverse iontophoretic procedure is performed.

Suppose that analysis of the extracted samples indicates that 20 nmolesof glucose and 10 μmoles of sodium are extracted across 1 cm² of skin in1 hour.

The extracted ratio (glucose/sodium) is 2×10⁻³.

Now this information could be used in the following way:

Assume, in this hypothetical patient, that the glucose level below whichhypoglycemia is a concern is 80 mg/dL (i:e., 4.4 mM).

This value corresponds to a molar ratio (glucose/sodium) of 33×10⁻³ inthe sub-dermal fluids assuming a constant sodium concentration of 133mM.

According to our in vitro results (by substitution in the regressionequation of FIG. 22 a), an extraction ratio of 2×10⁻³ indicates that theglucose concentration systemically is about 3.3 mM, i.e., the sub-dermal[glucose]/[sodium] ratio is 24.8×10⁻³ (FIG. 22 b).

We would conclude, therefore, that the glucose plasma levels of thispatient were too low.

In fact, the values assumed for this hypothetical patient correspondclosely to one of our in vitro experiments with a sub-dermal glucoseconcentration of 3 mM and a [mannitol]/[sodium] ratio of 22.5×10⁻³.

In other words, there is a good predictive value of the equationsdeveloped.

A similar exercise could be performed, self-evidently, for a patientexperiencing hyperglycemia (i.e., plasma glucose levels above a certainupper limit).

It is further important to reiterate that FIGS. 22 a-b demonstrate thedetermination of the constants K and K′ necessary to calculate anabsolute concentration of an analyte in the biological system from theextracted ratio of the analyte to the chosen internal standard.

In this example, the chosen analyte (A) is glucose, while the internalstandard (B) is Na⁺.

According to Equation 1, therefore,Qglu/QNa⁺ =K.[glu]/[Na⁺]

K can be read from the slope of the graph in FIG. 22 b; that is,following a period of iontophoresis of 6 hours at 0.5 mA/cm², K=0.076.

It is noteworthy that the corresponding value for mannitol, in thisExample, is 0.078.

Similarly, according to Equation 2,Qglu/QNa⁺ =K′.[glu]

K′ can be read from the slope of the graph in FIG. 22 a and is equal toK divided by the fixed Na⁺ concentration (133 mM) in the biologicalsystem.

Following a period of iontophoresis of 6 hours at 0.5 mA/cm²,K′=0.572×10⁻³.

Note that the corresponding value for mannitol, in this Example, is0.586×10⁻³.

It follows that, once the value of K′ has been established for aparticular pair of substances, and given that the concentration of theinternal standard ([B]) in the biological system is constant, thenEquation 2 can be used to determine the concentration of the analyte ofinterest ([A]) directly from the iontophoretic extraction ratio Qa/Qb.

Finally, the linearity of the relationship established by the data inFIG. 22 c indicates the possibility of using an uncharged molecule as aninternal standard for an analyte which is also uncharged.

Example 7

A series of in vitro experiments was performed in specifically-designediontophoresis diffusion cells (Laboratory Glass Apparatus, Berkeley,Calif., USA) as represented in FIG. 23.

The sub-dermal (donor) solution was a pH 7.4 buffer (25 mM Hepes+133 mMNaCl) to which the analyte of interest, the anti-manic drug lithium (asthe chloride salt) was added at one of 3 different concentrations: 1.37mM, 0.86 mM, 0.45 mM.

Sodium ion was the chosen internal standard.

The anodal and cathodal chambers contacted the outer surface of the skinand contained the receptor (collection) media, respectively, 133 mMNaCl+25 mM Hepes and 10 mM KCl+25 mM Hepes (both buffered at pH 7.4).

Full-thickness pig-ear skin was clamped between the two halves of theiontophoresis cell and each chamber filled with the appropriatesolution.

A schema of the experiment is shown in FIG. 23.

A current of 0.4 mA (0.5 mA/cm²) was passed between silver-silverchloride, (Ag/AgCl) electrodes, inserted into the anodal and cathodalchambers, for a total of 5 hours.

Every hour, the entire content of the cathode solution was withdrawn andthe chamber refilled with fresh buffer.

All samples were analyzed for lithium by atomic absorption spectroscopyand for sodium using an ion-selective electrode.

Three replicates were performed for each lithium concentration.

FIGS. 24 a-b show the (a) the extraction fluxes of lithium and sodium,and (b) the (lithium/sodium) extraction flux ratios, over the 5 hours ofexperiment, for each sub-dermal lithium concentration considered.

Table XV also presents the extracted flux ratios (lithium/sodium), as afunction of time, for each of the different sub-dermal concentrationratios (lithium/sodium) considered.

FIGS. 25 a-b show the correlation between the iontophoretic extractionratio of lithium to sodium and [a] the lithium sub-dermal concentration,and [b] the sub-dermal concentration ratio (lithium/sodium) over the5-hour period of the experiment.

TABLE XV Extracted flux ratios (×10³) for lithium and sodium ions.Values are mean ± standard deviation. (10³×) Extracted (lithium/Na⁺)flux ratio (10³×) Subdermal [lithium]/[Na⁺] ratio Time (min) 3.4 6.510.3 60 0.71 ± 0.28 1.48 ± 0.41 2.28 ± 0.43 120 1.38 ± 0.19 2.65 ± 0.554.45 ± 0.64 180 1.54 ± 0.20 3.13 ± 0.78 5.25 ± 0.48 240 1.80 ± 0.03 2.79± 0.35 5.64 ± 0.52 300 1.62 ± 0.03 3.13 ± 0.51 5.45 ± 0.36

To illustrate how this technique would work in practice, consider somepractical situations using the information and relationships obtainedfrom the experiments described above.

Consider a patient taking lithium, whose plasma sodium concentration is133 mM, and on whom a reverse iontophoretic procedure is performed.

Suppose that analysis of the extracted samples indicates that theextracted ratio (lithium/sodium) is 1×10⁻³.

Now this information could be used in the following way:

Assume a therapeutic range for lithium of 0.5-1.4 mM.

Such values correspond to molar ratios (lithium/sodium) of 3.76×10⁻³ and10.5×10⁻³ in the sub-dermal fluids.

According to our in vitro results (by substitution in the regressionequation obtained at 5 hours, FIG. 25 b), an extraction ratio of 1×10⁻³indicates that the sub-dermal [lithium]/[sodium] ratio is less than3×10⁻³, i.e., that the sub-dermal lithium concentration is less than 0.4mM.

We would conclude, therefore, that the lithium plasma levels of thispatient were too low and out of the therapeutic range.

It is further important to reiterate that FIGS. 25 a-b demonstrate thedetermination of the constants K and K′ necessary to calculate anabsolute concentration of an analyte in the biological system from theextracted ratio of the analyte to the chosen internal standard.

In this example, the chosen analyte (A) is lithium, while the internalstandard (B) is sodium.

According to Equation 1, therefore,QLi/QNa=K.[Li]/[Na]

K is the slope of the graph in FIG. 25 b; that is, following a short(5-hour) period of iontophoresis at 0.5 mA/cm², K=0.56.

Similarly, according to Equation 2,QLi/QNa=K′.[Li]

K′ is the slope of the graph in FIG. 25 a and is equal to K divided bythe fixed sodium concentration (133 mM) in the biological system.

Following a short (5-hour) period of iontophoresis at 0.5 mA/cm²,K′=4.18×10⁻³.

It follows that, once the value of K′ has been established for aparticular pair of substances, and given that the concentration of theinternal standard ([B]) in the biological system is constant, thenEquation 2 can be used to determine the concentration of the analyte ofinterest ([A]) directly from the iontophoretic extraction ratio Qa/Qb.

Example 8

Two cylindrical glass cells (area=2 cm²) were fixed to the ventralsurface of a healthy volunteer's forearm. The distance between thechambers was approximately 8 cm.

The anode was positioned in one of the cells, which was filled with asolution containing a 10 mM Tris buffer pH 8.5+100 mM NaCl.

The other (collection) chamber contained the cathode submerged in a 10mM Tris buffer at pH 8.5.

The two electrodes were connected to a power supply (Phoresor II Auto,lomed, USA) and a current of 0.6 mA (0.3 mA/cm²) was passed between themfor a total of 5.5 hours.

The entire contents of the cathode solution were withdrawn every 15minutes and the chamber was then refilled with fresh buffer.

From the seventh collection period, the volunteer's blood sugarconcentration was measured at the beginning of each iontophoreticinterval. A droplet of capillary blood was collected from the finger tipand analyzed for glucose with the Glucotrend 2 monitor (RocheDiagnostics, Switzerland).

Glucose in each iontophoretic sample was analyzed by high-performanceanion-exchange chromatography with pulsed amperometric detection. Sodiumions were analyzed by an enzymatic β-galactosidase assay.

FIG. 26 shows the results obtained. The blood glucose concentrationsshown correspond to the average of the values measured at the beginningand at the end of each iontophoretic extraction period. Theiontophoretically extracted glucose flux mirrored very closely thechanges in blood sugar, increasing and then subsequently decreasingfollowing ingestion of food. On the other hand, the extraction flux ofNa⁺ remained effectively constant over the entire period of theexperiment, reflecting the fact that the systemic concentration of Na⁺is quite invariant in a living human being.

From the data in FIG. 26, it can be deduced that the ratio of theextracted flux of glucose divided by that of Na⁺ depended linearly onboth the blood concentration of glucose (C_(glu)):J _(glu) /J _(Na) ⁺=0.001*C _(glu)−(1.6×10⁴); r=0.87and on the ratio of the blood concentrations of glucose andNa⁺(C_(glu)/C_(Na+)):J _(glu) /J _(Na) ⁺=0.13*(C _(glu) /C _(Na+))+(7.2×10⁻⁵); r=0.87

The data illustrate in vivo, in man, therefore, the principal featuresof the invention disclosed.

1. A method for non-invasively determining the relative levels of twosubstances present in a biological system, said method comprisingcontacting an anodal chamber and a cathodal chamber of an iontophoresisdevice comprising reversible electrodes with a biological system;extracting by reverse iontophoresis charged and uncharged substancesfrom said biological system, and collecting said charged and unchargedsubstances each independently into the anodal chamber or the cathodalchamber; determining a first substance and a second substance from saidextracted charged and uncharged substances a) such that the firstsubstance is different from the second substance and b) such that i) atransport and/or a transference number of the first substance isindependent of ii) a transport and/or a transference number of thesecond substance; analysing the collected amount of the first substanceand the second substance; subsequently, determining the extraction ratioof the first substance to the second substance to determine theirrelative levels in the biological system; determining at least one of aphysiological and pathological condition based on the determinedextraction ratio and without requiring blood sampling for calibration.2. The method according to claim 1, characterised in that the electrodesof the iontophoretic device are silver/silver chloride electrodes. 3.The method according to claim 2, characterised in that the firstsubstance analysed and the second substance analysed are contained inthe same chamber.
 4. The method according to claim 3, characterised inthat the biological system is a human body.
 5. The method according toclaim 4, characterised in that the current density applied by theiontophoretic device during the iontophoretic extraction is not higherthan 0.5 mA/cm².
 6. The method according to claim 5, characterised inthat the determination of the extraction ratio of the first substance tothe second substance is made by calculating the ratio of the collectedamount of the first extracted substance to the collected amount of thesecond extracted substance.
 7. The method according to claim 5,characterised in that the determination of the extraction ratio of thefirst substance to the second substance is made by first calculating theflux of the first extracted substance and the flux of the secondsubstance, based on the extracted amount of the first substance and theextracted amount of the second substance, respectively, and then bycalculating the ratio of the flux of the first extracted substance tothe flux of the second extracted substance.
 8. The method according toclaim 7, characterised in that the analysis of the two selectedsubstances is made by techniques involving specific enzymes orbiosensors, ion-selective chemistry, measurement of conductivity, andall other known analytical chemistry techniques.
 9. The method accordingto claim 8, characterised in that the first and second analysedsubstances are susceptible to changes in their concentration in thebiological system.
 10. The method according to claim 8, characterised inthat the first analysed substance is susceptible to changes in itsconcentration in the biological system and the second analysed substancehas a substantially constant concentration in the biological system. 11.The method according to claim 10, characterised in that the firstsubstance is glucose.
 12. The method according to claim 10,characterised in that the first substance is lithium.
 13. The methodaccording to claim 12, characterised in that the second substance issodium.
 14. The method according to claim 13, characterised in thatelectrode polarity is reversed subsequent to each extraction/analysiscycle.
 15. A method for non-invasively determining the relative levelsof two substances present in a biological system, said method comprisingcontacting an anodal chamber and a cathodal chamber of an iontophoresisdevice having reversible electrodes with a biological system; extractingby reverse iontophoresis charged and uncharged substances from saidbiological system, and collecting said charged and uncharged substanceseach independently into the anodal chamber or the cathodal chamber;determining first and second substances from said extracted charged anduncharged substances a) such that i) a transport number and/or atransference number of the first substance is independent of ii) atransport number and/or a transference number of the second substance,and b) such that the second substance has a substantially constantconcentration in the biological system and acts as an internal standard;analysing the collected amount of the first extracted substance and thesecond extracted substance; and subsequently, determining an extractionratio of the first substance to the second substance to determine theirrelative levels in the biological system determining at least one of aphysiological and pathological condition based on the extraction ratio.